Семінар з диференціальних рівнянь

26 листопада о 15:05 відбудеться засідання Львівського міського семінару з диференціальних рівнянь.

Доповідач: Iryna Kmit (Humboldt University of Berlin, Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NASU)

Тема доповіді: Classical bounded and almost periodic solutions to quasilinear first-order hyperbolic systems

The boundary conditions are supposed to be of a smoothing type, in the sense that the $L^2$-generalized solutions to the initial-boundary value problems become eventually $C^2$-smooth for any $L^2$-initial data. We establish conditions for the existence and uniqueness of small bounded (globally in time) classical solutions if the right-hand sides are small. Specifically, we suppose the existence of the exponential dichotomy of the evolution family generated by the linearized problem. We prove that the dichotomy survives under small (unbounded) perturbations. Assuming that the coefficients of the hyperbolic system are (almost) periodic in time, we prove that the bounded solution is (almost) periodic in time also.

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